code: def test_forecast_correctness(self):
      observed_time_series_ = np.array([1.0, -1.0, -3.0, 4.0])
      observed_time_series = self._build_tensor(observed_time_series_)
      model = self._build_model(
          observed_time_series, constant_offset=0.0
      )  # Simplifies analytic calculations.
  
      drift_scale = 0.1
      observation_noise_scale = 0.01
      params = {
          "seasonal_drift_scale"
          if JAX_MODE
          else "seasonal/_drift_scale": self._build_tensor(
              [drift_scale]
          ),
          "observation_noise_scale": self._build_tensor(
              [observation_noise_scale]
          ),
      }
  
      @tf.function(autograph=False, jit_compile=tf.executing_eagerly())
      def _run():
          forecast_dist = forecast.forecast(
              model,
              observed_time_series,
              parameter_samples=params,
              num_steps_forecast=8,
              include_observation_noise=True,
          )
          return (
              forecast_dist.mean()[..., 0],
              forecast_dist.stddev()[..., 0],
          )
  
      forecast_mean, forecast_scale = _run()
  
      # Since Seasonal is just a set of interleaved random walks, it's
      # straightforward to compute the forecast analytically.
      effect_posterior_precision = (
          1.0 + 1 / observation_noise_scale**2
      )
      effect_posterior_means = (
          observed_time_series_ / observation_noise_scale**2
      ) / effect_posterior_precision
      effect_posterior_variance = 1 / effect_posterior_precision
      observation_predictive_variance = (
          effect_posterior_variance
          + drift_scale**2
          + observation_noise_scale**2
      )
  
      expected_forecast_mean = np.concatenate(
          [effect_posterior_means, effect_posterior_means]
      )
      expected_forecast_scale = np.concatenate(
          [
              [np.sqrt(observation_predictive_variance)] * 4,
              [
                  np.sqrt(
                      observation_predictive_variance + drift_scale**2
                  )
              ]
              * 4,
          ]
      )
      self.assertAllClose(forecast_mean, expected_forecast_mean)
      self.assertAllClose(forecast_scale, expected_forecast_scale)
  
      # Also test forecasting the noise-free function.
      forecast_dist = forecast.forecast(
          model,
          observed_time_series,
          parameter_samples=params,
          num_steps_forecast=8,
          include_observation_noise=False,
      )
      forecast_mean = forecast_dist.mean()[..., 0]
      forecast_scale = forecast_dist.stddev()[..., 0]
  
      noiseless_predictive_variance = (
          effect_posterior_variance + drift_scale**2
      )
      expected_forecast_scale = np.concatenate(
          [
              [np.sqrt(noiseless_predictive_variance)] * 4,
              [
                  np.sqrt(
                      noiseless_predictive_variance + drift_scale**2
                  )
              ]
              * 4,
          ]
      )
      self.assertAllClose(forecast_mean, expected_forecast_mean)
      self.assertAllClose(forecast_scale, expected_forecast_scale)
  
imports: import numpy
  import tensorflow.compat.v1
  import tensorflow.compat.v2
  from tensorflow_probability.python.distributions import normal
  from tensorflow_probability.python.internal import test_util
  from tensorflow_probability.python.sts import fitting
  from tensorflow_probability.python.sts import forecast
  from tensorflow_probability.python.sts.components import seasonal
  from tensorflow_probability.python.sts.components import sum
  from tensorflow_probability.python.sts.internal import missing_values_util
label_desc: Use image node_id 4 for calling the _ForecastTest obj's underlying member method code with example usage: obj.test_forecast_correctness() and returns: forecast_dist,  forecast_dist